President Zine El Abidine Ben Ali, facing weeks of riots that have posed the toughest challenge to his regime in 23 years, promised that the early elections would take place within six months, the official TAP news agency reported.
He made no reference, however, to any resignation of his own.
Protesters mobbed the capital of Tunis on Friday, fueled by pent-up anger at high unemployment and at a leadership many see as controlling and corrupt. Marching through the city, they demanded Ben Ali's resignation and some even climbed onto the roof of the Interior Ministry _ a symbol of his repressive regime.
Many shouted "Ben Ali, out!" and "Ben Ali, assassin!" Another poster read "We won't forget," a reference to the rioters killed, many by police bullets.
Helmeted police were seen kicking and clubbing unarmed protesters _ one of whom cowered on the ground, covering his face. A few youths were spotted throwing stones at police.
The demonstrators were of all ages and from all walks of life.
"A month ago, we didn't believe this uprising was possible," said Beya Mannai, a geology professor at the University of Tunis. "But the people rose up." Thousands of tourists, meanwhile, were evacuated from the North African tourist haven.
The new unrest came just a day after Ben Ali tried to quell the uproar by going on television to promise lower food prices and new freedoms for Tunisians.
Ben Ali, 74, has maintained an iron grip on Tunisia since grabbing power in 1987 in a bloodless coup, repressing any challenges. He has locked up many opposition figures, clamped down on dissent and kept tight control over the media but has not been able to resolve the country's rising unemployment, officially at nearly 14 percent, but higher for educated youths.
The unrest began after an educated but jobless 26-year-old committed suicide in mid-December when police confiscated the fruits and vegetables he was selling without a permit.
His desperate act hit a nerve, sparked copycat suicides and focused generalized anger against the regime into a widespread, outright revolt.
The official death toll in the riots is 23, but opposition leaders put the figure at three times that, and medical workers on Friday reported another 13 new deaths and over 50 injuries from late Thursday alone. Police have repeatedly fired on crowds with bullets.
U.S. diplomatic cables released by WikiLeaks have called Tunisia a "police state" and described the corruption there, and social networks like Facebook have helped spread the comments. Many ordinary Tunisians who have complained for years felt vindicated to see the U.S. diplomatic cables.